Quantum mechanics by itself is not an answer. A ray in a Hilbert space looks less like the world than does a scattering of particles in a three-dimensional space. At least the latter still has forms with size and shape. The significance of quantum mechanics is that conscious experiences are complex wholes, and so are entangled states. So a quantum ontology in which reality consists of an evolving network of states drawn from Hilbert spaces of very different dimensionalities, has the potential to be describing conscious states with very high-dimensional tensor factors, and an ambient neural environment of small, decohered quantum systems (e.g. most biomolecules) with a large number of small-dimensional tensor factors. Rather than seeing large tensor factors as an entanglement of many particles, we would see "particles" as what you get when a tensor factor shrinks to its smallest form.

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Once this is done, the way you state the laws of motion might change. Instead of saying 'tensor factor T with neighbors T0...Tn has probability p of being replaced by Tprime', you would say 'conscious state C, causally adjacent to microphysical objects P0...Pn, has probability p of evolving into conscious state Cprime' - where C and Cprime are described in a "pure-phenomenological" way, by specifying sensory, intentional, reflective, and whatever other ingredients are needed to specify a subjective state exactly.

You are hitting the nail in the head. I don't expect people in LessWrong to understand this for a while, though. There is actually a good reason why the cognitive style of rationalists, at least statistically, is particularly ill-suited for making sense of the properties of subjective experience and how they constrain the range of possible philosophies of mind. The main problem is the axis of variability of "empathizer vs. systematizer." LessWrong is built on a highly systematizing meme-plex that attracts people who have a motivational architecture particularly well suited for problems that require systematizing intelligence.

Unfortunately, recognizing that one's consciousness is ontologically unitary requires a lot of introspection and trusting one's deepest understanding against the conclusions that one's working ontology suggests. Since LessWrongers have been trained to disregard their own intuitions and subjective experience when thinking about the nature of reality, it makes sense that the unity of consciousness will be a blind spot for as long as we don't come up with experiments that can show the causal relevance of such unity. My hope is to find a computational task that consciousness can achieve at a runtime complexity that would be impossible with a classical neural networks implemented with the known physical constraints of the brain. However, I'm not very optimistic this will happen any time soon.

The alternative is to lay out specific testable predictions involving the physical implementation of consciousness in the brain. I recommend reading David Pearce's physicalism.com, which outlines an experiment that would convince any rational eternal quantum mind skeptic that indeed the brain is a quantum computer.